question_answer

A 26 m long ladder reached a window 24 m from the ground on placing it against a wall. Find the distance of the foot of the ladder from the wall.

A)  \[10\,m\]                     

B)  \[20\,m\]         

C)         \[5\,m\]           

D)         \[25\,m\]                     

Correct Answer: A

Solution :

In  \[\Delta PRQ,\] \[P{{R}^{2}}=P{{Q}^{2}}+Q{{R}^{2}}\]             (By Pythagoras theorem)    \[{{(26)}^{2}}={{(24)}^{2}}+Q{{R}^{2}}\] or \[Q{{R}^{2}}=676-576=100\] \[\Rightarrow \] \[QR=\sqrt{100}\Rightarrow QR=10\] \[\therefore \] The distance of the foot of the ladder from the wall is 10 m.